Reachability sets of hybrid systems in the presence of successive switchings

The concept of reachability domains of hybrid systems is described together with the use of ellipsoidal methods for calculation of such domains in the case when there are successive switchings on several given hyperplanes or bands. An algorithm for calculation of the reachability sets for a hybrid system that uses ellipsoidal approximations is given for the cases in which the switching sets are planes or bands. The parametrization of nonconvex reachability domains is obtained as a union of intersections of the corresponding ellipsoidal estimates.